[Phys-L] Re: buoyancy

[John Denker <jsd@AV8N.COM>]

Anthony Lapinski wrote:
> Objects float in water because the weight of the displaced
> water equals the object's weight. I put a beaker of water on a
> scale and ask my students what will happen to the reading if I
> dip my hand in. Most say it will stay the same, but are
> surprised to find the reading actually increases -- by the
> weight of displaced water my finger pushes away. I ask if a
> live fish were placed in the water, would the reading change?
> Yes -- by the weight of displaced water once again. But what
> if the fish dies and goes to the bottom of the beaker? The
> scale reading should reflect this. It should increase by the
> actual weight of the fish. But does the weight of displaced
> water matter?
>
> I tried this with a golf ball, each weighed (massed)
> separately. When I dropped the ball in, the scale only
> increased by the ball's weight. There is still a buoyant force
> upward, and this balances the (downward) weight of displaced
> water. So the reading should only increase by the object's
> weight. Is this correct reasoning?

Simpler reasoning woult start by noting that mass is
conserved. So the mass of water plus ball will be
the sum of the masses of the constituents. You don't
need to know anything about buoyancy to know this.


But cross-checking can't hurt and might help, so we can
cross-check the previous argument against a buoyancy-based
argument, as follows:

The force on the beaker is the sum of the weight of the
stuff resting on it. Buoyancy causes the golf-ball to push
against the bottom in a water-filled beaker with markedly
less force than it would in a dry beaker. This effect is
exactly compensated by the increase in hydrostatic force,
which will be larger with than without the ball, due to
the displaced volume.